Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
Points M and P lie on square LNQR, and LM = PQ. What is the length of the line segment PQ?
(1) PR=410 − − √ 3
(2) The ratio of the area of the unshaded region to the total area of the shaded region is 2 to 1.
We can know PQ if we know PR, so there is one variable (PR), and 2 equations are given by the conditions, so there is high chance (D) will be the answer.
For condition 1, from (4 sqrt 10/3)^2-4^2=PQ^2. PQ=4/3. This is sufficient
For condition 2, if the ratio of the area is 2:1, the height is the same, so NP:PQ=2:1, and PQ=4/3 so this is sufficient as well, and the answer becomes (D).
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.